Paper 56: Idioms are Oblivious, Arrows are Meticulous, Monads are Promiscuous

Rongmin Lu will take us through the following paper:

Idioms are Oblivious, Arrows are Meticulous, Monads are Promiscuous
Sam Lindley, PhilipWadler, Jeremy Yallop

Abstract

We revisit the connection between three notions of computation: Moggiʼs monads, Hughesʼs arrows and McBride and Patersonʼs idioms (also called applicative functors). We show that idioms are equivalent to arrows that satisfy the type isomorphism A ↝ B ≃ 1 →(A ↝ B)
and that monads are equivalent to arrows that satisfy the type isomorphism A ↝ B ≃ A→(1 ↝ B). Further, idioms embed into arrows and arrows embed into monads.